Circumsphere Radius Of Truncated Rhombohedron Given Total Surface Area Calculator

Formula Used:

\[ r_c = \frac{\sqrt{14 - 2\sqrt{5}}}{4} \times \sqrt{\frac{2 \times TSA}{3\sqrt{5 + 2\sqrt{5}} + 5\sqrt{3} - 2\sqrt{15}}} \]

Circumsphere Radius (r_c):

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1. What is Circumsphere Radius of Truncated Rhombohedron?

The Circumsphere Radius of a Truncated Rhombohedron is the radius of the sphere that contains the polyhedron in such a way that all the vertices are lying on the sphere. It represents the distance from the center of the polyhedron to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \frac{\sqrt{14 - 2\sqrt{5}}}{4} \times \sqrt{\frac{2 \times TSA}{3\sqrt{5 + 2\sqrt{5}} + 5\sqrt{3} - 2\sqrt{15}}} \]

Where:

\( r_c \) — Circumsphere Radius (m)
\( TSA \) — Total Surface Area of Truncated Rhombohedron (m²)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the circumsphere radius based on the total surface area of the truncated rhombohedron, incorporating various mathematical constants and operations.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in geometry and 3D modeling for understanding the spatial dimensions and properties of truncated rhombohedrons, particularly in crystallography and material science applications.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Truncated Rhombohedron?
A: A truncated rhombohedron is a polyhedron obtained by cutting the corners of a rhombohedron, resulting in a shape with both triangular and hexagonal faces.

Q2: What units should I use for input?
A: The calculator expects the total surface area in square meters (m²). Ensure consistent units throughout your calculations.

Q3: Can this calculator handle very large or small values?
A: The calculator can handle a wide range of values, but extremely large or small numbers may affect computational precision.

Q4: What are typical values for circumsphere radius?
A: The circumsphere radius depends on the size of the truncated rhombohedron. For a unit truncated rhombohedron, the circumsphere radius is approximately 0.95 units.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the given formula, assuming accurate input values and proper implementation of the mathematical operations.